Convergence analysis of Davidchack and Lai's algorithm for finding periodic orbits

DOI10.1016/S0960-0779(00)00099-0zbMath1024.37020OpenAlexW1996761923MaRDI QIDQ1862333

Erik M. Bollt, Aaron Klebanoff

Publication date: 19 March 2003

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(00)00099-0

zbMATH Keywords

basin of attractionNewton methodnumerical algorithmswitching matrixhyperbolic periodic orbits

Mathematics Subject Classification ID

Periodic orbits of vector fields and flows (37C27) Dynamical systems with hyperbolic orbits and sets (37D05) Numerical nonlinear stabilities in dynamical systems (65P40)

Related Items (4)

Complexified stable and unstable manifolds and chaotic tunneling ⋮ Finite-time braiding exponents ⋮ On comparing dynamical systems by defective conjugacy: A symbolic dynamics interpretation of commuter functions ⋮ Systematic computer assisted proofs of periodic orbits of Hamiltonian systems

Uses Software

• Dynamics

Cites Work

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• Dynamical averaging in terms of periodic orbits
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Periodic orbits as the skeleton of classical and quantum chaos
• Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems
• Generic diffeomorphisms with superexponential growth of number of periodic orbits
• From template analysis to generating partitions. I: Periodic orbits, knots and symbolic encodings
• From template analysis to generating partitions. II: Characterization of the symbolic encodings
• Recycling of strange sets: I. Cycle expansions
• Symplectic maps, variational principles, and transport
• On the efficiency of algorithms of analysis
• Pruning fronts and the formation of horseshoes
• The fundamental theorem of algebra and complexity theory
• Measures on periodic orbits for continuous transformations on the interval
• Some systems with unique equilibrium states
• A Measure Associated with Axiom-A Attractors
• A Turning Point Analysis of the Ergodic Dynamics of Iterative Maps
• The convergence of chaotic integrals
• Characterization of unstable periodic orbits in chaotic attractors and repellers
• Differentiable dynamical systems
• Periodic Points and Measures for Axiom a Diffeomorphisms
• Periodic Orbits for Hyperbolic Flows
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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